Garcia's Grill offers 8 side dishes, 4 types of steak, and 5 toppings. How many different...

Garcia's Grill offers 8 side dishes, 4 types of steak, and 5 toppings. How many different smothered steak dinners can be made if a smothered steak dinner consists of the customer's choice of steak served with 2 different toppings and 4 different side dishes?

Expert Solution

Answer:

Garcia's Grill offers 8 side dishes, 4 types of steak and 5 toppings

Now a smothered steak dinner consists of 1 steak served with 2 different toppings and 4 different side dishes

To find out how many different smothered steak dinners can be made we will use combinatorics

Number of ways the 1 steak can be selected from 4 types of steaks

= 4C1 =4 [as we are selecting 1 out of 4]

Number of ways 4 different side dishes can be selected from 8 types of side dishes= 8C4= 70 [as we are selecting 4 out of 8]

Number of ways 2 different toppings can be selected from 5 types of toppings= 5C2= 10 [as we are selecting 2 out of 5]

To find how many different smothered steak dinners can be made we multiply number of ways each item can be selected

Number of different smothered steak dinners can be made = 4C1 * 8C4 * 4C2 = 4*70*10 = 2800

Answer: 2800 different smothered steak dinners can be made

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orchestra answered 1 year ago

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